Two topics in 2D quantum field theory

Citation

Abstract

Two topics in two-dimensional quantum field theory are presented. The first
is a classification of 2- and 3-field rational conformal field theories. Using the fact
that the fusion algebra of a RCFT is specified in terms of integers that are related
to modular transformation properties, we classify 2- and 3-field chiral RCFT's. We
show that the only possibilities for the non-trivial fusion rule in the 2-field case are
φ x φ = 1 or φ x φ = 1 + φ. Similar results are obtained for the 3-field case. A partial
classification of possible conformal dimensions and central charges for these theories
is also obtained. The second topic is in two-dimensional quantum gravity. Explicit
computation of the non-perturbative correlation functions of the (1, q) models of
KdV-gravity is presented. This computation includes contributions from high genus
as well as correlation functions of descendant fields. A ghost number conservation
law for these models is derived from purely algebraic considerations. A hint of further
selection rules is found.